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Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
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EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
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ICONIP'10 Proceedings of the 17th international conference on Neural information processing: theory and algorithms - Volume Part I
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The quadratic multiple knapsack problem extends the quadratic knapsack problem with K knapsacks, each with its own capacity Ck. A greedy heuristic fills the knapsacks one at a time with objects whose contributions are likely to be large relative to their weights. A hill-climber and a genetic algorithm encode candidate solutions as strings over {0,1,...,K} with length equal to the number of objects. The hill-climber's neighbor operator is also the GA's mutation. In tests on 60 problem instances, the GA performed better than the greedy heuristic on the smaller instances, but it fell behind as the numbers of objects and knapsacks grew. The hill-climber always outperformed the greedy heuristic, and on the larger instances, also the GA.